geometry.bundle_weights

geometry.bundle_weights(M, TM, method, reduce)

Computes geometrically informative statistics about a given tangent bundle.

This function computes a geometrically-derived statistic about a given tangent space TM using its neighborhood information. Such measures can at times be useful for constructing nerve complexes, removing outliers, detecting locally smooth areas, etc.

The methods supported include ‘distance’, ‘cosine’, and ‘angle’, which do the following:

    * 'distance': Measures the distance from each neighborhood point to its projection onto the tangent space using the Euclidean norm.
    * 'cosine': Measures the distance from each neighborhood tangent vector to a fixed tangent vector using the cosine distance. 
    * 'angle': Measures the distance from each neighborhood tangent vector to a fixed tangent vector using the stiefel canonical metric. 

Parameters

Name	Type	Description	Default
M	sparray	Sparse matrix whose columns represent subsets of X.	required
TM	list	Tangent bundle, given as a list of (base point, tangent vector) pairs	required
method	str	geometric quantity to compute, one of {'distance', 'cosine', 'angle'}. Defaults to ‘cosine’.	required
reduce	Union[str, Callable]	aggregation function to compute the final statistic. Defaults to the average (see details).	required

Returns

Type	Description
np.ndarray	the aggregate statistic for each tangent space, given as an array of weights.